A 12-year annuity pays $1,400 per month, and payments are made at the end of each...

A 12-year annuity pays $1,400 per month, and payments are made at the end of each month. The interest rate is 11 percent compounded monthly for the first six years and 10 percent compounded monthly thereafter. What is the present value of the annuity?

Expert Solution

Monthly payment = $1,400

Time period = 12 years or 144 months

Annual interest rate for first 6 years = 11.00%
Monthly interest rate for first 6 years = 11.00% / 12
Monthly interest rate for first 6 years = 0.91667%

Annual interest rate for next 6 years = 10.00%
Monthly interest rate for next 6 years = 10.00% / 12
Monthly interest rate for next 6 years = 0.83333%

Value of annuity at the end of 6 years = $1,400/1.0083333 + $1,400/1.0083333^2 + … + $1,400/1.0083333^71 + $1,400/1.0083333^72
Value of annuity at the end of 6 years = $1,400 * (1 - (1/1.0083333)^72) / 0.0083333
Value of annuity at the end of 6 years = $1,400 * 53.978724
Value of annuity at the end of 6 years = $75,570.2136

Present value of annuity = $1,400/1.0091667 + $1,400/1.0091667^2 + … + $1,400/1.0091667^71 + $1,400/1.0091667^72 + $75,570.2136/1.0091667^72
Present value of annuity = $1,400 * (1 - (1/1.0091667)^72) / 0.0091667 + $75,570.2136 * (1/1.0091667)^72
Present value of annuity = $1,400 * 52.537290 + $75,570.2136 * 0.518406
Present value of annuity = $112,728.26

jeff jeffy answered 1 year ago

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